The mod 2 cohomology of the infinite families of Coxeter groups of type B and D as almost Hopf rings

We describe a Hopf ring structure on the direct sum of the cohomology groups $\bigoplus_{n \geq 0} H^* \left( B_n; \mathbb{Z}_2 \right)$ of the Coxeter groups of type $B_n$, and an almost-Hopf ring structure on the direct sum of the cohomology groups $\bigoplus_{n \geq 0} H^* \left( D_n; \mathbb{Z}_2 \right)$ of the Coxeter groups of type $D_n$, with coefficient in the field with two elements $\mathbb{Z}_2$. We give presentations with generators and relations, determine additive bases and compute the Steenrod algebra action. The generators are described both in terms of a geometric construction by De Concini and Salvetti and in terms of their restriction to elementary abelian 2-subgroups.Comment: 32 page

What do English language teachers need to know about English as an International Language?

Some applied linguists have provided a definition of English as an international language (EIL) in order to distinguish it from other concepts such as English as a foreign language (EFL) or English as a second language (ESL). Whereas EFL and ESL have usually been related to non-native speakers of English communicating with native speakers of English, English as an international language can be defined as “that English in all its linguistic and sociolinguistic aspects which is used as a vehicle for communication between non-native speakers only, as well as between any combination of native and non-native speakers.” (Campbell et al. 1983) In other words, EIL aims at mutual intelligibility and appropriate language use involving nationals of different countries. Essentially, the concept of EIL focuses on cross-cultural, cross-linguistic interactions. In order to identify the major features of EIL, Campbell et al. (1983) introduced three principles of teaching EIL (TEIL): (1) knowledge of the different social and cultural patterns and rules present in communicative exchanges involving speakers of more than one country or culture; (2) training native speakers in the use of English in international contexts; and (3) training non-native speakers in the use of language with native as well as with non-native speakers. This paper aims at dealing with some pedagogical implications of TEIL in Portuguese basic and secondary schools. In spite of recent changes in ELT in Portugal, there are still some common ideas based on linguistic and pedagogical fallacies. Through the proposal of a TEIL paradigm, this paper will point out some of these fallacies hoping to generate ample debate on the new directions in ELT worldwide and in Portugal

The replica symmetric behavior of the analogical neural network

In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we introduce and apply a new interpolation scheme to its free energy that naturally extends the interpolation via cavity fields or stochastic perturbations to these models. As a result we obtain the free energy of the system as a sum rule, which, at least at the replica symmetric level, can be solved exactly. As a next step we study its related self-consistent equations for the order parameters and their rescaled fluctuations, found to diverge on the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page

Essays on delegation and social norms

This thesis presents the results of my doctoral studies at Middlesex University London. It contains different papers related to Labour Markets and presents some results on production, delegation and dishonest behaviour. The first study compares how group size interacts with both constrained and un-constrained resource environments, finding that resource limitations diminish production over time and that all the groups learn with experience. The second explores the effects of incentives in dishonest behaviour in both the gain and loss domain finding that contrary to theoretical predictions, subjects do not cheat more when they are facing a loss. The third, studies the distributions derived from different delegation scenarios. We find that the distributions derived from optional delegation are more egalitarian than the ones made under compulsory delegation. Finally, I study gender differences in delegation finding that gender biases only arise in compulsory delegation, and not under endogenous delegation, and at an agent level